X*x+(x-2)*(x-2)=10*10

Solution for X*x+(x-2)*(x-2)=10*10 equation:

X*X+(X-2)(X-2)=10*10

We move all terms to the left:

X*X+(X-2)(X-2)-(10*10)=0

We add all the numbers together, and all the variables

X*X+(X-2)(X-2)-100=0

Wy multiply elements

X^2+(X-2)(X-2)-100=0

We multiply parentheses ..

X^2+(+X^2-2X-2X+4)-100=0

We get rid of parentheses

X^2+X^2-2X-2X+4-100=0

We add all the numbers together, and all the variables

2X^2-4X-96=0

a = 2; b = -4; c = -96;
Δ = b2-4ac
Δ = -42-4·2·(-96)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*2}=\frac{-24}{4}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*2}=\frac{32}{4}
=8
$